We present a general method for computing local parameterizations rooted at a point on a surface, where the surface is described only through a signed implicit function and a corresponding projection function. Using a two-stage process, we compute several points radially emanating from the map origin, and interpolate between them with a spline surface. The narrow interface of our method allows it to support several kinds of geometry such as signed distance functions, general analytic implicit functions, triangle meshes, neural implicits, and point clouds. We demonstrate the high quality of our generated parameterizations on a variety of examples, and show applications in local texturing and surface curve drawing.
@inproceedings{Madan:2025:local-parameterizations,
author = {Madan, Abhishek and Levin, David I.W.},
title = {Local Surface Parameterizations via Smoothed Geodesic Splines},
journal = {ACM Trans. Graph. (to appear)},
year = {2025},
publisher = {ACM}
}
This project was funded in part by an NSERC Discovery Grant (RGPIN-2023–05120) and an Ontario Early Researchers Award. The first author was funded by an NSERC Canada Graduate Scholarship — Doctoral. We thank Victor Rong, Honglin Chen, Silvia Sellán, and Towaki Takikawa for proofreading.